Would it be okay to say "mopping a sidewalk" when a sidewalk is being cleaned with water and mops or is there a better and a more common way of describing this action?
There are two ways to answer this question. Literally, yes, you can mop a sidewalk by using a mop to scrub it, but it probably wouldn't be very good for the mop.
Idiomatically, it would be better to simply say you're washing or washing down the sidewalk, usually just with a hose and something like a push-broom to sweep up any debris.
Every morning (except when it rained) the owner of the corner grocery would wash down the sidewalk in front of her store.
If not explicitly stated, "washing" implies the gentle use of water to wash away dirt and debris. If you want to really clean the sidewalk, you need to use a power washer / pressure hose
Side note: "Sidewalk" is American English. In British English that particular part of the road is called a "pavement", and in Australian English it's called a "footpath". This can be confusing, since in American English the "pavement" usually refers to the paved part of the road where cars drive.
Mops are for floors inside buildings. Mops are not generally used to clean sidewalks. Mops are dipped in a bucket of water, squeezed out and then dragged across the floor. That is known as damp mopping.
Sidewalks are swept with brooms by a person or cleaned by machine with a variety of configurations of water and/or brushes.